Analyse Factorielle Exploratoire
library(tidyverse) # Manipulation des données
library(readxl) # Lecture des fichiers Excel
library(ggpubr) # Représentations graphiques
library(rstatix) # Tests statistiques en langage Dplyr
library(corrplot) # Corrélogrammes
library(plotly) # Graphes intéractifs
library(psych)
library(EFAtools)
library(shiny)Avec toutes les variables quantitatives
Données
Pré-requis
Bartlett
bartlett.test(dataComp %>% select(where(is.numeric)))
Bartlett test of homogeneity of variances
data: dataComp %>% select(where(is.numeric))
Bartlett's K-squared = 564.07, df = 41, p-value < 2.2e-16KMO
KMO(dataComp %>% select(where(is.numeric)))ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.
── Kaiser-Meyer-Olkin criterion (KMO) ────────────────────────────────────
✔ The overall KMO value for your data is meritorious.
These data are probably suitable for factor analysis.
Overall: 0.841
For each variable:
AFE1 AFE2 AFE4 AFE5 AFP1 AFP2 AFP3 AFP4 AFP5 AFP6 CF1 CF2
0.772 0.401 0.741 0.577 0.881 0.791 0.909 0.883 0.850 0.887 0.922 0.775
CF3 CF4 CF5 CF6 CF7 CF8 IEIP1 IEIP2 IEIP3 IEIP4 LDS1 LDS2
0.836 0.845 0.877 0.889 0.928 0.844 0.760 0.899 0.876 0.584 0.398 0.831
LDS3 LDS4 LDS5 LDS6 MOT1 MOT21 MOT3 MOT4 MOT5 MOT6 MOT7 MOT8
0.644 0.726 0.508 0.668 0.870 0.905 0.916 0.883 0.912 0.847 0.923 0.884
MOT9 NSUB1 NSUB2 NSUB3 NSUB4 NSUB5
0.907 0.580 0.678 0.490 0.555 0.751 Nombre de facteurs
fa.parallel(dataComp, fa="fa", fm="pa")Parallel analysis suggests that the number of factors = 7 and the number of components = NA 
Modélisation
2 Facteurs
Modèle
fit2 <- fa(dataComp, nfactors = 2, rotate = "oblimin", fm = "pa", use = "pairwise")
print(fit2)Factor Analysis using method = pa
Call: fa(r = dataComp, nfactors = 2, rotate = "oblimin", fm = "pa",
use = "pairwise")
Standardized loadings (pattern matrix) based upon correlation matrix
PA1 PA2
SS loadings 7.61 3.67
Proportion Var 0.18 0.09
Cumulative Var 0.18 0.27
Proportion Explained 0.67 0.33
Cumulative Proportion 0.67 1.00
With factor correlations of
PA1 PA2
PA1 1.00 0.54
PA2 0.54 1.00
Mean item complexity = 1.3
Test of the hypothesis that 2 factors are sufficient.
The degrees of freedom for the null model are 861 and the objective function was 18.17 with Chi Square of 3037.23
The degrees of freedom for the model are 778 and the objective function was 7.89
The root mean square of the residuals (RMSR) is 0.07
The df corrected root mean square of the residuals is 0.08
The harmonic number of observations is 183 with the empirical chi square 1683.87 with prob < 9.4e-69
The total number of observations was 183 with Likelihood Chi Square = 1308.74 with prob < 1.2e-29
Tucker Lewis Index of factoring reliability = 0.727
RMSEA index = 0.061 and the 90 % confidence intervals are 0.055 0.067
BIC = -2744.24
Fit based upon off diagonal values = 0.91
Measures of factor score adequacy
PA1 PA2
Correlation of (regression) scores with factors 0.96 0.93
Multiple R square of scores with factors 0.92 0.86
Minimum correlation of possible factor scores 0.85 0.72Loadings
print(fit2$loadings, sort = T, cutoff = 0.4)
Loadings:
PA1 PA2
AFP3 0.649
AFP4 0.531
AFP5 0.581
CF4 0.767
CF5 0.592
CF7 0.584
IEIP2 0.733
IEIP3 0.548
MOT21 0.535
MOT3 0.657
MOT7 0.536
MOT8 0.621
MOT9 0.543
AFP1 0.728
AFP2 0.591
AFP6 0.744
CF6 0.521
AFE1
AFE2
AFE4
AFE5 -0.426
CF1 0.469
CF2
CF3 0.457
CF8
IEIP1
IEIP4
LDS1
LDS2
LDS3
LDS4
LDS5
LDS6
MOT1
MOT4 0.492
MOT5 0.489
MOT6 0.495
NSUB1
NSUB2 -0.411
NSUB3
NSUB4
NSUB5 0.465
PA1 PA2
SS loadings 7.190 3.250
Proportion Var 0.171 0.077
Cumulative Var 0.171 0.249Diagramme
fa.diagram(fit2, digits = 2)
3 Facteurs
Modèle
fit3 <- fa(dataComp, nfactors = 3, rotate = "oblimin", fm = "pa", use = "pairwise")
print(fit3)Factor Analysis using method = pa
Call: fa(r = dataComp, nfactors = 3, rotate = "oblimin", fm = "pa",
use = "pairwise")
Standardized loadings (pattern matrix) based upon correlation matrix
PA1 PA2 PA3
SS loadings 7.54 3.72 1.63
Proportion Var 0.18 0.09 0.04
Cumulative Var 0.18 0.27 0.31
Proportion Explained 0.58 0.29 0.13
Cumulative Proportion 0.58 0.87 1.00
With factor correlations of
PA1 PA2 PA3
PA1 1.00 0.50 -0.12
PA2 0.50 1.00 -0.04
PA3 -0.12 -0.04 1.00
Mean item complexity = 1.6
Test of the hypothesis that 3 factors are sufficient.
The degrees of freedom for the null model are 861 and the objective function was 18.17 with Chi Square of 3037.23
The degrees of freedom for the model are 738 and the objective function was 7
The root mean square of the residuals (RMSR) is 0.06
The df corrected root mean square of the residuals is 0.07
The harmonic number of observations is 183 with the empirical chi square 1267.66 with prob < 1.4e-30
The total number of observations was 183 with Likelihood Chi Square = 1155.88 with prob < 5.2e-21
Tucker Lewis Index of factoring reliability = 0.772
RMSEA index = 0.055 and the 90 % confidence intervals are 0.05 0.062
BIC = -2688.72
Fit based upon off diagonal values = 0.93
Measures of factor score adequacy
PA1 PA2 PA3
Correlation of (regression) scores with factors 0.96 0.93 0.83
Multiple R square of scores with factors 0.92 0.87 0.69
Minimum correlation of possible factor scores 0.84 0.73 0.38Loadings
print(fit3$loadings, sort = T, cutoff = 0.4)
Loadings:
PA1 PA2 PA3
AFP3 0.639
AFP4 0.528
AFP5 0.572
CF4 0.758
CF5 0.586
CF7 0.574
IEIP2 0.718
IEIP3 0.541
MOT21 0.529
MOT3 0.648
MOT6 0.504
MOT7 0.529
MOT8 0.621
MOT9 0.539
AFP1 0.704
AFP2 0.665
AFP6 0.776
NSUB1 -0.532
AFE1
AFE2
AFE4
AFE5
CF1 0.473
CF2
CF3 0.449
CF6 0.476
CF8
IEIP1
IEIP4
LDS1
LDS2 -0.410
LDS3
LDS4
LDS5 0.423
LDS6
MOT1
MOT4 0.484
MOT5 0.485
NSUB2
NSUB3
NSUB4
NSUB5 0.457
PA1 PA2 PA3
SS loadings 7.048 3.224 1.620
Proportion Var 0.168 0.077 0.039
Cumulative Var 0.168 0.245 0.283Diagramme
fa.diagram(fit3, digits = 2)
4 Facteurs
Modèle
fit4 <- fa(dataComp, nfactors = 4, rotate = "oblimin", fm = "pa", use = "pairwise")
print(fit4)Factor Analysis using method = pa
Call: fa(r = dataComp, nfactors = 4, rotate = "oblimin", fm = "pa",
use = "pairwise")
Standardized loadings (pattern matrix) based upon correlation matrix
PA1 PA2 PA3 PA4
SS loadings 6.60 3.87 1.98 1.93
Proportion Var 0.16 0.09 0.05 0.05
Cumulative Var 0.16 0.25 0.30 0.34
Proportion Explained 0.46 0.27 0.14 0.13
Cumulative Proportion 0.46 0.73 0.87 1.00
With factor correlations of
PA1 PA2 PA3 PA4
PA1 1.00 0.48 0.29 0.20
PA2 0.48 1.00 0.18 0.17
PA3 0.29 0.18 1.00 0.07
PA4 0.20 0.17 0.07 1.00
Mean item complexity = 1.7
Test of the hypothesis that 4 factors are sufficient.
The degrees of freedom for the null model are 861 and the objective function was 18.17 with Chi Square of 3037.23
The degrees of freedom for the model are 699 and the objective function was 6.14
The root mean square of the residuals (RMSR) is 0.05
The df corrected root mean square of the residuals is 0.06
The harmonic number of observations is 183 with the empirical chi square 950.26 with prob < 6.5e-10
The total number of observations was 183 with Likelihood Chi Square = 1010.64 with prob < 9.1e-14
Tucker Lewis Index of factoring reliability = 0.82
RMSEA index = 0.049 and the 90 % confidence intervals are 0.043 0.056
BIC = -2630.79
Fit based upon off diagonal values = 0.95
Measures of factor score adequacy
PA1 PA2 PA3 PA4
Correlation of (regression) scores with factors 0.96 0.93 0.86 0.85
Multiple R square of scores with factors 0.92 0.87 0.74 0.72
Minimum correlation of possible factor scores 0.83 0.74 0.48 0.45Loadings
print(fit4$loadings, sort = T, cutoff = 0.4)
Loadings:
PA1 PA2 PA3 PA4
AFP3 0.653
AFP4 0.710
AFP5 0.622
CF4 0.688
CF5 0.548
IEIP2 0.631
MOT3 0.612
MOT5 0.508
MOT7 0.535
MOT8 0.802
AFP1 0.695
AFP2 0.711
AFP6 0.790
LDS2 0.562
LDS3 0.620
NSUB1 0.564
AFE1
AFE2
AFE4
AFE5 0.409
CF1 0.487
CF2
CF3
CF6 0.442
CF7
CF8
IEIP1
IEIP3 0.433
IEIP4 0.459
LDS1
LDS4 0.456
LDS5
LDS6
MOT1 0.423
MOT21 0.472
MOT4 0.442
MOT6 0.493
MOT9 0.486
NSUB2
NSUB3 0.474
NSUB4
NSUB5
PA1 PA2 PA3 PA4
SS loadings 5.869 3.306 1.826 1.768
Proportion Var 0.140 0.079 0.043 0.042
Cumulative Var 0.140 0.218 0.262 0.304Diagramme
fa.diagram(fit4, digits = 2)
5 Facteurs
Modèle
fit5 <- fa(dataComp, nfactors = 5, rotate = "oblimin", fm = "pa", use = "pairwise")
print(fit5)Factor Analysis using method = pa
Call: fa(r = dataComp, nfactors = 5, rotate = "oblimin", fm = "pa",
use = "pairwise")
Standardized loadings (pattern matrix) based upon correlation matrix
PA1 PA2 PA4 PA3 PA5
SS loadings 6.47 3.35 2.19 2.09 1.43
Proportion Var 0.15 0.08 0.05 0.05 0.03
Cumulative Var 0.15 0.23 0.29 0.34 0.37
Proportion Explained 0.42 0.22 0.14 0.13 0.09
Cumulative Proportion 0.42 0.63 0.77 0.91 1.00
With factor correlations of
PA1 PA2 PA4 PA3 PA5
PA1 1.00 0.45 0.26 0.31 0.01
PA2 0.45 1.00 0.27 0.20 -0.05
PA4 0.26 0.27 1.00 0.09 0.02
PA3 0.31 0.20 0.09 1.00 0.02
PA5 0.01 -0.05 0.02 0.02 1.00
Mean item complexity = 1.8
Test of the hypothesis that 5 factors are sufficient.
The degrees of freedom for the null model are 861 and the objective function was 18.17 with Chi Square of 3037.23
The degrees of freedom for the model are 661 and the objective function was 5.51
The root mean square of the residuals (RMSR) is 0.05
The df corrected root mean square of the residuals is 0.06
The harmonic number of observations is 183 with the empirical chi square 770.08 with prob < 0.0021
The total number of observations was 183 with Likelihood Chi Square = 903.09 with prob < 9.7e-10
Tucker Lewis Index of factoring reliability = 0.851
RMSEA index = 0.044 and the 90 % confidence intervals are 0.037 0.052
BIC = -2540.38
Fit based upon off diagonal values = 0.96
Measures of factor score adequacy
PA1 PA2 PA4 PA3
Correlation of (regression) scores with factors 0.96 0.93 0.87 0.87
Multiple R square of scores with factors 0.92 0.86 0.75 0.75
Minimum correlation of possible factor scores 0.83 0.72 0.50 0.50
PA5
Correlation of (regression) scores with factors 0.83
Multiple R square of scores with factors 0.69
Minimum correlation of possible factor scores 0.37Loadings
print(fit5$loadings, sort = T, cutoff = 0.4)
Loadings:
PA1 PA2 PA4 PA3 PA5
AFP3 0.644
AFP4 0.708
AFP5 0.613
CF4 0.692
CF5 0.540
IEIP2 0.630
MOT3 0.601
MOT5 0.500
MOT7 0.528
MOT8 0.785
AFE1 0.647
AFP1 0.733
AFP2 0.735
AFP6 0.654
MOT4 0.513
LDS2 0.562
LDS3 0.628
NSUB1 0.548
AFE5 0.519
NSUB3 0.516
AFE2
AFE4
CF1 0.430
CF2
CF3
CF6 0.489
CF7
CF8
IEIP1
IEIP3 0.427
IEIP4
LDS1
LDS4 0.475
LDS5
LDS6 0.423
MOT1 0.428
MOT21 0.463
MOT6 0.481
MOT9 0.478
NSUB2 0.442
NSUB4
NSUB5
PA1 PA2 PA4 PA3 PA5
SS loadings 5.725 2.823 1.815 1.890 1.415
Proportion Var 0.136 0.067 0.043 0.045 0.034
Cumulative Var 0.136 0.204 0.247 0.292 0.325Diagramme
fa.diagram(fit5, digits = 2)
6 Facteurs
Modèle
fit6 <- fa(dataComp, nfactors = 6, rotate = "oblimin", fm = "pa", use = "pairwise")
print(fit6)Factor Analysis using method = pa
Call: fa(r = dataComp, nfactors = 6, rotate = "oblimin", fm = "pa",
use = "pairwise")
Standardized loadings (pattern matrix) based upon correlation matrix
PA1 PA2 PA4 PA3 PA5 PA6
SS loadings 4.75 3.43 3.30 2.19 1.45 1.38
Proportion Var 0.11 0.08 0.08 0.05 0.03 0.03
Cumulative Var 0.11 0.19 0.27 0.33 0.36 0.39
Proportion Explained 0.29 0.21 0.20 0.13 0.09 0.08
Cumulative Proportion 0.29 0.50 0.70 0.83 0.92 1.00
With factor correlations of
PA1 PA2 PA4 PA3 PA5 PA6
PA1 1.00 0.39 0.45 0.27 0.00 0.06
PA2 0.39 1.00 0.38 0.22 -0.05 0.17
PA4 0.45 0.38 1.00 0.24 0.06 0.17
PA3 0.27 0.22 0.24 1.00 0.01 0.01
PA5 0.00 -0.05 0.06 0.01 1.00 0.01
PA6 0.06 0.17 0.17 0.01 0.01 1.00
Mean item complexity = 2.2
Test of the hypothesis that 6 factors are sufficient.
The degrees of freedom for the null model are 861 and the objective function was 18.17 with Chi Square of 3037.23
The degrees of freedom for the model are 624 and the objective function was 5.01
The root mean square of the residuals (RMSR) is 0.05
The df corrected root mean square of the residuals is 0.05
The harmonic number of observations is 183 with the empirical chi square 639.66 with prob < 0.32
The total number of observations was 183 with Likelihood Chi Square = 816.82 with prob < 2.9e-07
Tucker Lewis Index of factoring reliability = 0.874
RMSEA index = 0.041 and the 90 % confidence intervals are 0.033 0.049
BIC = -2433.89
Fit based upon off diagonal values = 0.96
Measures of factor score adequacy
PA1 PA2 PA4 PA3
Correlation of (regression) scores with factors 0.94 0.93 0.90 0.87
Multiple R square of scores with factors 0.88 0.86 0.82 0.76
Minimum correlation of possible factor scores 0.76 0.72 0.64 0.53
PA5 PA6
Correlation of (regression) scores with factors 0.83 0.83
Multiple R square of scores with factors 0.69 0.68
Minimum correlation of possible factor scores 0.38 0.36Loadings
print(fit6$loadings, sort = T, cutoff = 0.4)
Loadings:
PA1 PA2 PA4 PA3 PA5 PA6
AFP4 0.671
AFP5 0.547
CF4 0.525
MOT3 0.509
MOT7 0.518
MOT8 0.738
AFE1 0.670
AFP1 0.732
AFP2 0.719
AFP6 0.639
CF6 0.514
IEIP3 0.595
NSUB5 0.581
LDS2 0.581
LDS3 0.640
NSUB1 0.543
AFE5 0.526
LDS6 0.509
AFE2
AFE4
AFP3 0.400 0.462
CF1 0.432
CF2
CF3
CF5
CF7
CF8
IEIP1
IEIP2 0.447
IEIP4
LDS1
LDS4 0.467
LDS5
MOT1
MOT21
MOT4 0.460
MOT5
MOT6 0.448
MOT9 0.470
NSUB2 0.460
NSUB3 0.495
NSUB4
PA1 PA2 PA4 PA3 PA5 PA6
SS loadings 3.875 2.851 2.477 1.956 1.432 1.252
Proportion Var 0.092 0.068 0.059 0.047 0.034 0.030
Cumulative Var 0.092 0.160 0.219 0.266 0.300 0.330Diagramme
fa.diagram(fit6, digits = 2)
7 Facteurs
Modèle
fit7 <- fa(dataComp, nfactors = 7, rotate = "oblimin", fm = "pa", use = "pairwise")Warning: convergence not obtained in GPFoblq. 1000 iterations used.print(fit7)Factor Analysis using method = pa
Call: fa(r = dataComp, nfactors = 7, rotate = "oblimin", fm = "pa",
use = "pairwise")
Standardized loadings (pattern matrix) based upon correlation matrix
PA1 PA7 PA2 PA3 PA5 PA6 PA4
SS loadings 4.35 3.62 3.20 1.81 1.54 1.51 1.41
Proportion Var 0.10 0.09 0.08 0.04 0.04 0.04 0.03
Cumulative Var 0.10 0.19 0.27 0.31 0.35 0.38 0.42
Proportion Explained 0.25 0.21 0.18 0.10 0.09 0.09 0.08
Cumulative Proportion 0.25 0.46 0.64 0.74 0.83 0.92 1.00
With factor correlations of
PA1 PA7 PA2 PA3 PA5 PA6 PA4
PA1 1.00 0.54 0.35 0.19 0.08 0.26 0.06
PA7 0.54 1.00 0.40 0.17 0.11 0.24 0.13
PA2 0.35 0.40 1.00 0.14 -0.01 0.22 0.13
PA3 0.19 0.17 0.14 1.00 0.03 0.14 -0.02
PA5 0.08 0.11 -0.01 0.03 1.00 0.06 0.04
PA6 0.26 0.24 0.22 0.14 0.06 1.00 0.07
PA4 0.06 0.13 0.13 -0.02 0.04 0.07 1.00
Mean item complexity = 2.3
Test of the hypothesis that 7 factors are sufficient.
The degrees of freedom for the null model are 861 and the objective function was 18.17 with Chi Square of 3037.23
The degrees of freedom for the model are 588 and the objective function was 4.49
The root mean square of the residuals (RMSR) is 0.04
The df corrected root mean square of the residuals is 0.05
The harmonic number of observations is 183 with the empirical chi square 522.59 with prob < 0.98
The total number of observations was 183 with Likelihood Chi Square = 730.28 with prob < 5.4e-05
Tucker Lewis Index of factoring reliability = 0.9
RMSEA index = 0.036 and the 90 % confidence intervals are 0.027 0.045
BIC = -2332.9
Fit based upon off diagonal values = 0.97
Measures of factor score adequacy
PA1 PA7 PA2 PA3
Correlation of (regression) scores with factors 0.94 0.92 0.93 0.86
Multiple R square of scores with factors 0.88 0.86 0.86 0.74
Minimum correlation of possible factor scores 0.75 0.71 0.71 0.47
PA5 PA6 PA4
Correlation of (regression) scores with factors 0.84 0.82 0.84
Multiple R square of scores with factors 0.71 0.67 0.70
Minimum correlation of possible factor scores 0.41 0.33 0.40Loadings
print(fit7$loadings, sort = T, cutoff = 0.4)
Loadings:
PA1 PA7 PA2 PA3 PA5 PA6 PA4
AFP4 0.608
AFP5 0.646
MOT21 0.501
MOT7 0.561
MOT8 0.778
IEIP3 0.516
MOT9 0.745
AFE1 0.610
AFP1 0.721
AFP2 0.738
AFP6 0.653
LDS3 0.521
NSUB1 0.622
AFE5 0.503
NSUB3 0.542
AFE2
AFE4
AFP3 0.472
CF1
CF2
CF3 0.445
CF4
CF5 0.458
CF6 0.400 0.425
CF7
CF8
IEIP1
IEIP2 0.454
IEIP4
LDS1
LDS2 0.442
LDS4 0.499
LDS5 -0.457
LDS6 0.440
MOT1 0.403
MOT3
MOT4
MOT5
MOT6 0.480
NSUB2 0.442
NSUB4
NSUB5
PA1 PA7 PA2 PA3 PA5 PA6 PA4
SS loadings 3.478 2.690 2.678 1.683 1.500 1.227 1.304
Proportion Var 0.083 0.064 0.064 0.040 0.036 0.029 0.031
Cumulative Var 0.083 0.147 0.211 0.251 0.286 0.316 0.347Diagramme
fa.diagram(fit7, digits = 2)
Fiabilité
alpha(dataComp)Warning: Some items were negatively correlated with the total scale and probably
should be reversed.
To do this, run the function again with the 'check.keys=TRUE' optionSome items ( AFE5 LDS5 NSUB2 ) were negatively correlated with the total scale and
probably should be reversed.
To do this, run the function again with the 'check.keys=TRUE' option
Reliability analysis
Call: alpha(x = dataComp)
95% confidence boundaries
Reliability if an item is dropped:
Item statistics
Non missing response frequency for each item
1 2 3 4 5 miss
AFE1 0.03 0.07 0.50 0.21 0.18 0
AFE2 0.08 0.18 0.41 0.22 0.11 0
AFE4 0.05 0.09 0.15 0.28 0.43 0
AFE5 0.21 0.39 0.22 0.14 0.04 0
AFP1 0.02 0.08 0.50 0.24 0.16 0
AFP2 0.08 0.12 0.47 0.22 0.11 0
AFP3 0.01 0.05 0.15 0.34 0.46 0
AFP4 0.01 0.02 0.06 0.36 0.56 0
AFP5 0.01 0.02 0.10 0.28 0.58 0
AFP6 0.02 0.07 0.49 0.30 0.12 0
CF1 0.02 0.03 0.13 0.45 0.37 0
CF2 0.07 0.34 0.25 0.27 0.08 0
CF3 0.02 0.03 0.13 0.30 0.53 0
CF4 0.01 0.02 0.05 0.27 0.64 0
CF5 0.01 0.01 0.04 0.35 0.59 0
CF6 0.03 0.09 0.36 0.27 0.26 0
CF7 0.02 0.04 0.21 0.46 0.27 0
CF8 0.04 0.13 0.26 0.43 0.13 0
IEIP1 0.01 0.01 0.03 0.47 0.49 0
IEIP2 0.02 0.03 0.07 0.28 0.60 0
IEIP3 0.02 0.08 0.18 0.38 0.34 0
IEIP4 0.10 0.11 0.28 0.31 0.20 0
LDS1 0.42 0.58 0.00 0.00 0.00 0
LDS2 0.04 0.07 0.25 0.43 0.21 0
LDS3 0.02 0.07 0.67 0.19 0.05 0
LDS4 0.04 0.10 0.52 0.27 0.07 0
LDS5 0.17 0.31 0.34 0.15 0.03 0
LDS6 0.04 0.20 0.38 0.22 0.15 0
MOT1 0.02 0.08 0.46 0.30 0.14 0
MOT21 0.01 0.02 0.10 0.58 0.29 0
MOT3 0.01 0.02 0.04 0.50 0.44 0
MOT4 0.04 0.10 0.40 0.30 0.16 0
MOT5 0.01 0.04 0.22 0.48 0.25 0
MOT6 0.02 0.00 0.02 0.26 0.70 0
MOT7 0.01 0.01 0.09 0.46 0.44 0
MOT8 0.01 0.01 0.01 0.29 0.69 0
MOT9 0.03 0.02 0.16 0.39 0.40 0
NSUB1 0.02 0.03 0.41 0.39 0.15 0
NSUB2 0.12 0.32 0.46 0.09 0.02 0
NSUB3 0.22 0.32 0.25 0.17 0.04 0
NSUB4 0.11 0.16 0.26 0.31 0.16 0
NSUB5 0.05 0.08 0.23 0.38 0.25 0Avec le retrait : AFE, NSUB, LDS
Données
Pré-requis
Bartlett
bartlett.test(dataComp %>% select(where(is.numeric)))
Bartlett test of homogeneity of variances
data: dataComp %>% select(where(is.numeric))
Bartlett's K-squared = 292.4, df = 26, p-value < 2.2e-16KMO
KMO(dataComp %>% select(where(is.numeric)))ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.
── Kaiser-Meyer-Olkin criterion (KMO) ────────────────────────────────────
✔ The overall KMO value for your data is marvellous.
These data are probably suitable for factor analysis.
Overall: 0.907
For each variable:
AFP1 AFP2 AFP3 AFP4 AFP5 AFP6 CF1 CF2 CF3 CF4 CF5 CF6
0.886 0.807 0.929 0.908 0.895 0.878 0.945 0.823 0.829 0.873 0.927 0.916
CF7 CF8 IEIP1 IEIP2 IEIP3 IEIP4 MOT1 MOT21 MOT3 MOT4 MOT5 MOT6
0.930 0.893 0.842 0.931 0.929 0.635 0.877 0.923 0.938 0.889 0.942 0.920
MOT7 MOT8 MOT9
0.956 0.901 0.926 Nombre de facteurs
fa.parallel(dataComp, fa="fa", fm="pa")Parallel analysis suggests that the number of factors = 3 and the number of components = NA 
Modélisation
2 Facteurs
Modèle
fit2 <- fa(dataComp, nfactors = 2, rotate = "oblimin", fm = "pa", use = "pairwise")
print(fit2)Factor Analysis using method = pa
Call: fa(r = dataComp, nfactors = 2, rotate = "oblimin", fm = "pa",
use = "pairwise")
Standardized loadings (pattern matrix) based upon correlation matrix
PA1 PA2
SS loadings 7.03 3.14
Proportion Var 0.26 0.12
Cumulative Var 0.26 0.38
Proportion Explained 0.69 0.31
Cumulative Proportion 0.69 1.00
With factor correlations of
PA1 PA2
PA1 1.00 0.51
PA2 0.51 1.00
Mean item complexity = 1.2
Test of the hypothesis that 2 factors are sufficient.
The degrees of freedom for the null model are 351 and the objective function was 12.18 with Chi Square of 2097.64
The degrees of freedom for the model are 298 and the objective function was 2.83
The root mean square of the residuals (RMSR) is 0.06
The df corrected root mean square of the residuals is 0.06
The harmonic number of observations is 183 with the empirical chi square 423.43 with prob < 2.3e-06
The total number of observations was 183 with Likelihood Chi Square = 483.61 with prob < 5.4e-11
Tucker Lewis Index of factoring reliability = 0.874
RMSEA index = 0.058 and the 90 % confidence intervals are 0.049 0.068
BIC = -1068.82
Fit based upon off diagonal values = 0.97
Measures of factor score adequacy
PA1 PA2
Correlation of (regression) scores with factors 0.96 0.93
Multiple R square of scores with factors 0.92 0.87
Minimum correlation of possible factor scores 0.84 0.74Loadings
print(fit2$loadings, sort = T, cutoff = 0.4)
Loadings:
PA1 PA2
AFP3 0.661
AFP4 0.623
AFP5 0.606
CF4 0.780
CF5 0.630
IEIP2 0.707
IEIP3 0.514
MOT21 0.546
MOT3 0.694
MOT5 0.532
MOT6 0.543
MOT7 0.535
MOT8 0.736
MOT9 0.545
AFP1 0.638
AFP2 0.700
AFP6 0.867
CF1 0.492
CF2
CF3 0.409
CF6 0.412
CF7 0.491
CF8
IEIP1
IEIP4
MOT1 0.434
MOT4
PA1 PA2
SS loadings 6.570 2.689
Proportion Var 0.243 0.100
Cumulative Var 0.243 0.343Diagramme
fa.diagram(fit2, digits = 2)
3 Facteurs
Modèle
fit3 <- fa(dataComp, nfactors = 3, rotate = "oblimin", fm = "pa", use = "pairwise")
print(fit3)Factor Analysis using method = pa
Call: fa(r = dataComp, nfactors = 3, rotate = "oblimin", fm = "pa",
use = "pairwise")
Standardized loadings (pattern matrix) based upon correlation matrix
PA1 PA2 PA3
SS loadings 5.68 3.34 2.06
Proportion Var 0.21 0.12 0.08
Cumulative Var 0.21 0.33 0.41
Proportion Explained 0.51 0.30 0.19
Cumulative Proportion 0.51 0.81 1.00
With factor correlations of
PA1 PA2 PA3
PA1 1.00 0.48 0.43
PA2 0.48 1.00 0.32
PA3 0.43 0.32 1.00
Mean item complexity = 1.5
Test of the hypothesis that 3 factors are sufficient.
The degrees of freedom for the null model are 351 and the objective function was 12.18 with Chi Square of 2097.64
The degrees of freedom for the model are 273 and the objective function was 2.38
The root mean square of the residuals (RMSR) is 0.05
The df corrected root mean square of the residuals is 0.05
The harmonic number of observations is 183 with the empirical chi square 300.36 with prob < 0.12
The total number of observations was 183 with Likelihood Chi Square = 405.06 with prob < 3.5e-07
Tucker Lewis Index of factoring reliability = 0.901
RMSEA index = 0.051 and the 90 % confidence intervals are 0.041 0.062
BIC = -1017.13
Fit based upon off diagonal values = 0.98
Measures of factor score adequacy
PA1 PA2 PA3
Correlation of (regression) scores with factors 0.95 0.93 0.85
Multiple R square of scores with factors 0.90 0.87 0.73
Minimum correlation of possible factor scores 0.81 0.75 0.46Loadings
print(fit3$loadings, sort = T, cutoff = 0.4)
Loadings:
PA1 PA2 PA3
AFP3 0.502
AFP4 0.734
AFP5 0.578
CF4 0.663
IEIP2 0.536
MOT3 0.633
MOT6 0.567
MOT8 0.815
AFP1 0.675
AFP2 0.689
AFP6 0.863
CF1 0.517
MOT4 0.545
CF2
CF3
CF5 0.480
CF6 0.459
CF7 0.445
CF8
IEIP1
IEIP3
IEIP4 0.427
MOT1 0.433
MOT21 0.457
MOT5 0.402
MOT7 0.485
MOT9
PA1 PA2 PA3
SS loadings 4.909 2.808 1.542
Proportion Var 0.182 0.104 0.057
Cumulative Var 0.182 0.286 0.343Diagramme
fa.diagram(fit3, digits = 2)
4 Facteurs
Modèle
fit4 <- fa(dataComp, nfactors = 4, rotate = "oblimin", fm = "pa", use = "pairwise")
print(fit4)Factor Analysis using method = pa
Call: fa(r = dataComp, nfactors = 4, rotate = "oblimin", fm = "pa",
use = "pairwise")
Standardized loadings (pattern matrix) based upon correlation matrix
PA3 PA1 PA2 PA4
SS loadings 3.89 3.85 2.95 1.14
Proportion Var 0.14 0.14 0.11 0.04
Cumulative Var 0.14 0.29 0.40 0.44
Proportion Explained 0.33 0.33 0.25 0.10
Cumulative Proportion 0.33 0.65 0.90 1.00
With factor correlations of
PA3 PA1 PA2 PA4
PA3 1.00 0.59 0.43 0.24
PA1 0.59 1.00 0.38 0.32
PA2 0.43 0.38 1.00 0.21
PA4 0.24 0.32 0.21 1.00
Mean item complexity = 1.8
Test of the hypothesis that 4 factors are sufficient.
The degrees of freedom for the null model are 351 and the objective function was 12.18 with Chi Square of 2097.64
The degrees of freedom for the model are 249 and the objective function was 1.98
The root mean square of the residuals (RMSR) is 0.04
The df corrected root mean square of the residuals is 0.05
The harmonic number of observations is 183 with the empirical chi square 221.97 with prob < 0.89
The total number of observations was 183 with Likelihood Chi Square = 335.62 with prob < 2e-04
Tucker Lewis Index of factoring reliability = 0.929
RMSEA index = 0.043 and the 90 % confidence intervals are 0.031 0.055
BIC = -961.55
Fit based upon off diagonal values = 0.98
Measures of factor score adequacy
PA3 PA1 PA2 PA4
Correlation of (regression) scores with factors 0.92 0.93 0.93 0.80
Multiple R square of scores with factors 0.85 0.87 0.87 0.64
Minimum correlation of possible factor scores 0.71 0.74 0.75 0.28Loadings
print(fit4$loadings, sort = T, cutoff = 0.4)
Loadings:
PA3 PA1 PA2 PA4
CF7 0.626
MOT4 0.604
MOT9 0.501
AFP4 0.711
AFP5 0.705
MOT6 0.507
MOT8 0.759
AFP1 0.631
AFP2 0.676
AFP6 0.865
AFP3 0.417
CF1 0.421
CF2
CF3
CF4 0.429
CF5 0.499
CF6
CF8
IEIP1 0.445
IEIP2 0.463
IEIP3 0.496
IEIP4 0.455
MOT1 0.404
MOT21 0.471
MOT3 0.409
MOT5
MOT7 0.410
PA3 PA1 PA2 PA4
SS loadings 3.011 3.034 2.486 0.946
Proportion Var 0.112 0.112 0.092 0.035
Cumulative Var 0.112 0.224 0.316 0.351Diagramme
fa.diagram(fit4, digits = 2)
5 Facteurs
Modèle
fit5 <- fa(dataComp, nfactors = 5, rotate = "oblimin", fm = "pa", use = "pairwise")
print(fit5)Factor Analysis using method = pa
Call: fa(r = dataComp, nfactors = 5, rotate = "oblimin", fm = "pa",
use = "pairwise")
Standardized loadings (pattern matrix) based upon correlation matrix
PA1 PA5 PA2 PA3 PA4
SS loadings 3.33 3.24 2.94 1.82 1.23
Proportion Var 0.12 0.12 0.11 0.07 0.05
Cumulative Var 0.12 0.24 0.35 0.42 0.46
Proportion Explained 0.27 0.26 0.23 0.14 0.10
Cumulative Proportion 0.27 0.52 0.76 0.90 1.00
With factor correlations of
PA1 PA5 PA2 PA3 PA4
PA1 1.00 0.60 0.37 0.37 0.29
PA5 0.60 1.00 0.36 0.32 0.31
PA2 0.37 0.36 1.00 0.34 0.29
PA3 0.37 0.32 0.34 1.00 0.13
PA4 0.29 0.31 0.29 0.13 1.00
Mean item complexity = 2
Test of the hypothesis that 5 factors are sufficient.
The degrees of freedom for the null model are 351 and the objective function was 12.18 with Chi Square of 2097.64
The degrees of freedom for the model are 226 and the objective function was 1.65
The root mean square of the residuals (RMSR) is 0.04
The df corrected root mean square of the residuals is 0.04
The harmonic number of observations is 183 with the empirical chi square 165.46 with prob < 1
The total number of observations was 183 with Likelihood Chi Square = 277.81 with prob < 0.011
Tucker Lewis Index of factoring reliability = 0.953
RMSEA index = 0.035 and the 90 % confidence intervals are 0.018 0.049
BIC = -899.53
Fit based upon off diagonal values = 0.99
Measures of factor score adequacy
PA1 PA5 PA2 PA3
Correlation of (regression) scores with factors 0.93 0.92 0.93 0.85
Multiple R square of scores with factors 0.86 0.85 0.87 0.71
Minimum correlation of possible factor scores 0.71 0.70 0.74 0.43
PA4
Correlation of (regression) scores with factors 0.82
Multiple R square of scores with factors 0.68
Minimum correlation of possible factor scores 0.35Loadings
print(fit5$loadings, sort = T, cutoff = 0.4)
Loadings:
PA1 PA5 PA2 PA3 PA4
CF4 0.762
CF5 0.510
IEIP2 0.519
MOT9 0.540
AFP4 0.572
AFP5 0.657
MOT6 0.537
MOT8 0.746
AFP1 0.651
AFP2 0.677
AFP6 0.838
MOT4 0.612
IEIP1 0.666
AFP3 0.438
CF1 0.406
CF2
CF3
CF6 0.445
CF7 0.454
CF8
IEIP3 0.499
IEIP4
MOT1
MOT21 0.466
MOT3
MOT5
MOT7 0.404
PA1 PA5 PA2 PA3 PA4
SS loadings 2.417 2.472 2.459 1.352 1.001
Proportion Var 0.090 0.092 0.091 0.050 0.037
Cumulative Var 0.090 0.181 0.272 0.322 0.359Diagramme
fa.diagram(fit5, digits = 2)
6 Facteurs
Modèle
fit6 <- fa(dataComp, nfactors = 6, rotate = "oblimin", fm = "pa", use = "pairwise")
print(fit6)Factor Analysis using method = pa
Call: fa(r = dataComp, nfactors = 6, rotate = "oblimin", fm = "pa",
use = "pairwise")
Standardized loadings (pattern matrix) based upon correlation matrix
PA5 PA1 PA2 PA3 PA6 PA4
SS loadings 3.36 3.30 2.66 1.42 1.28 1.23
Proportion Var 0.12 0.12 0.10 0.05 0.05 0.05
Cumulative Var 0.12 0.25 0.34 0.40 0.44 0.49
Proportion Explained 0.25 0.25 0.20 0.11 0.10 0.09
Cumulative Proportion 0.25 0.50 0.70 0.81 0.91 1.00
With factor correlations of
PA5 PA1 PA2 PA3 PA6 PA4
PA5 1.00 0.58 0.34 0.30 0.21 0.30
PA1 0.58 1.00 0.37 0.34 0.25 0.31
PA2 0.34 0.37 1.00 0.21 0.34 0.27
PA3 0.30 0.34 0.21 1.00 0.17 0.05
PA6 0.21 0.25 0.34 0.17 1.00 0.18
PA4 0.30 0.31 0.27 0.05 0.18 1.00
Mean item complexity = 2
Test of the hypothesis that 6 factors are sufficient.
The degrees of freedom for the null model are 351 and the objective function was 12.18 with Chi Square of 2097.64
The degrees of freedom for the model are 204 and the objective function was 1.34
The root mean square of the residuals (RMSR) is 0.03
The df corrected root mean square of the residuals is 0.04
The harmonic number of observations is 183 with the empirical chi square 114.56 with prob < 1
The total number of observations was 183 with Likelihood Chi Square = 224.54 with prob < 0.15
Tucker Lewis Index of factoring reliability = 0.979
RMSEA index = 0.023 and the 90 % confidence intervals are 0 0.041
BIC = -838.19
Fit based upon off diagonal values = 0.99
Measures of factor score adequacy
PA5 PA1 PA2 PA3
Correlation of (regression) scores with factors 0.92 0.93 0.93 0.82
Multiple R square of scores with factors 0.85 0.86 0.86 0.67
Minimum correlation of possible factor scores 0.71 0.72 0.71 0.34
PA6 PA4
Correlation of (regression) scores with factors 0.83 0.82
Multiple R square of scores with factors 0.69 0.68
Minimum correlation of possible factor scores 0.38 0.36Loadings
print(fit6$loadings, sort = T, cutoff = 0.4)
Loadings:
PA5 PA1 PA2 PA3 PA6 PA4
AFP4 0.592
AFP5 0.690
MOT6 0.520
MOT8 0.730
CF4 0.684
IEIP3 0.514
MOT9 0.669
AFP1 0.709
AFP2 0.716
AFP6 0.765
IEIP4 0.612
MOT1 0.566
IEIP1 0.674
AFP3 0.462
CF1
CF2
CF3
CF5 0.486
CF6
CF7 0.466
CF8
IEIP2 0.451
MOT21 0.477
MOT3
MOT4 0.435
MOT5
MOT7 0.423
PA5 PA1 PA2 PA3 PA6 PA4
SS loadings 2.571 2.372 2.202 1.118 0.962 1.010
Proportion Var 0.095 0.088 0.082 0.041 0.036 0.037
Cumulative Var 0.095 0.183 0.265 0.306 0.342 0.379Diagramme
fa.diagram(fit6, digits = 2)
7 Facteurs
Modèle
fit7 <- fa(dataComp, nfactors = 7, rotate = "oblimin", fm = "pa", use = "pairwise")
print(fit7)Factor Analysis using method = pa
Call: fa(r = dataComp, nfactors = 7, rotate = "oblimin", fm = "pa",
use = "pairwise")
Standardized loadings (pattern matrix) based upon correlation matrix
PA1 PA2 PA5 PA6 PA4 PA7 PA3
SS loadings 2.74 2.74 2.15 1.92 1.84 1.25 1.10
Proportion Var 0.10 0.10 0.08 0.07 0.07 0.05 0.04
Cumulative Var 0.10 0.20 0.28 0.35 0.42 0.47 0.51
Proportion Explained 0.20 0.20 0.16 0.14 0.13 0.09 0.08
Cumulative Proportion 0.20 0.40 0.55 0.69 0.83 0.92 1.00
With factor correlations of
PA1 PA2 PA5 PA6 PA4 PA7 PA3
PA1 1.00 0.32 0.42 0.33 0.42 0.28 0.25
PA2 0.32 1.00 0.28 0.45 0.28 0.28 0.10
PA5 0.42 0.28 1.00 0.32 0.49 0.28 0.13
PA6 0.33 0.45 0.32 1.00 0.20 0.20 0.20
PA4 0.42 0.28 0.49 0.20 1.00 0.22 0.21
PA7 0.28 0.28 0.28 0.20 0.22 1.00 0.03
PA3 0.25 0.10 0.13 0.20 0.21 0.03 1.00
Mean item complexity = 2.5
Test of the hypothesis that 7 factors are sufficient.
The degrees of freedom for the null model are 351 and the objective function was 12.18 with Chi Square of 2097.64
The degrees of freedom for the model are 183 and the objective function was 1.15
The root mean square of the residuals (RMSR) is 0.03
The df corrected root mean square of the residuals is 0.04
The harmonic number of observations is 183 with the empirical chi square 93.41 with prob < 1
The total number of observations was 183 with Likelihood Chi Square = 192.94 with prob < 0.29
Tucker Lewis Index of factoring reliability = 0.989
RMSEA index = 0.016 and the 90 % confidence intervals are 0 0.038
BIC = -760.39
Fit based upon off diagonal values = 0.99
Measures of factor score adequacy
PA1 PA2 PA5 PA6
Correlation of (regression) scores with factors 0.91 0.93 0.90 0.87
Multiple R square of scores with factors 0.83 0.86 0.82 0.76
Minimum correlation of possible factor scores 0.67 0.72 0.64 0.51
PA4 PA7 PA3
Correlation of (regression) scores with factors 0.87 0.82 0.80
Multiple R square of scores with factors 0.75 0.68 0.64
Minimum correlation of possible factor scores 0.50 0.35 0.29Loadings
print(fit7$loadings, sort = T, cutoff = 0.4)
Loadings:
PA1 PA2 PA5 PA6 PA4 PA7 PA3
CF4 0.670
MOT9 0.567
AFP1 0.728
AFP2 0.731
AFP6 0.759
MOT8 0.777
MOT1 0.643
AFP5 0.612
IEIP1 0.647
IEIP4 0.651
AFP3 0.417
AFP4 0.474
CF1
CF2
CF3
CF5 0.433
CF6
CF7
CF8
IEIP2 0.439
IEIP3 0.444
MOT21
MOT3
MOT4 0.469
MOT5
MOT6
MOT7
PA1 PA2 PA5 PA6 PA4 PA7 PA3
SS loadings 1.915 2.247 1.430 1.342 1.215 1.009 0.941
Proportion Var 0.071 0.083 0.053 0.050 0.045 0.037 0.035
Cumulative Var 0.071 0.154 0.207 0.257 0.302 0.339 0.374Diagramme
fa.diagram(fit7, digits = 2)
Fiabilité
alpha(dataComp)
Reliability analysis
Call: alpha(x = dataComp)
95% confidence boundaries
Reliability if an item is dropped:
Item statistics
Non missing response frequency for each item
1 2 3 4 5 miss
AFP1 0.02 0.08 0.50 0.24 0.16 0
AFP2 0.08 0.12 0.47 0.22 0.11 0
AFP3 0.01 0.05 0.15 0.34 0.46 0
AFP4 0.01 0.02 0.06 0.36 0.56 0
AFP5 0.01 0.02 0.10 0.28 0.58 0
AFP6 0.02 0.07 0.49 0.30 0.12 0
CF1 0.02 0.03 0.13 0.45 0.37 0
CF2 0.07 0.34 0.25 0.27 0.08 0
CF3 0.02 0.03 0.13 0.30 0.53 0
CF4 0.01 0.02 0.05 0.27 0.64 0
CF5 0.01 0.01 0.04 0.35 0.59 0
CF6 0.03 0.09 0.36 0.27 0.26 0
CF7 0.02 0.04 0.21 0.46 0.27 0
CF8 0.04 0.13 0.26 0.43 0.13 0
IEIP1 0.01 0.01 0.03 0.47 0.49 0
IEIP2 0.02 0.03 0.07 0.28 0.60 0
IEIP3 0.02 0.08 0.18 0.38 0.34 0
IEIP4 0.10 0.11 0.28 0.31 0.20 0
MOT1 0.02 0.08 0.46 0.30 0.14 0
MOT21 0.01 0.02 0.10 0.58 0.29 0
MOT3 0.01 0.02 0.04 0.50 0.44 0
MOT4 0.04 0.10 0.40 0.30 0.16 0
MOT5 0.01 0.04 0.22 0.48 0.25 0
MOT6 0.02 0.00 0.02 0.26 0.70 0
MOT7 0.01 0.01 0.09 0.46 0.44 0
MOT8 0.01 0.01 0.01 0.29 0.69 0
MOT9 0.03 0.02 0.16 0.39 0.40 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